A new method for exciting and detecting an ion cyclotron resonance (ICR) mass spectrum is proposed. The excitation consists of a time sequence of pulses of equal width, amplitude, and spacing, with pseudorandom phase variation. For a given mass/charge (m/z) range, the excitation can be tailored to excite, all, all but one, ..., two, or one m/z-value in the range. Since time-shared detection is simultaneous with excitation, the stochastic method provides greater selectivity in excitation, simplified phasing leading to increased mass resolution, more uniform peak heights, increased dynamic range, and truly simultaneous multiple-ion monitoring for MS/MS and other applications. Additional specific proposals include a method for reducing (by a factor of 20) the amount of memory needed to store FT-ICR mass spectra, various array processor applications, non-linear data sampling for more efficient data storage, improvements in phase correction, automated tune-up procedures, multidimensional spectral displays, and others.